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    Here's a sequences and series problem that me entire maths class just can't solve:
    An arithmetic series has the property that the sum of the first ten terms is half the sum of the first sixteen terms. Also the 4th term is 14. Find the first term and common difference.
    We cant seem to figure it out and so any help or suggestions would be appreciated!
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    (Original post by Carloscactus)
    Here's a sequences and series problem that me entire maths class just can't solve:
    An arithmetic series has the property that the sum of the first ten terms is half the sum of the first sixteen terms. Also the 4th term is 14. Find the first term and common difference.
    We cant seem to figure it out and so any help or suggestions would be appreciated!
    form two equations based on the standard formulas and solve them simultaneously
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    (Original post by Carloscactus)
    Here's a sequences and series problem that me entire maths class just can't solve:
    An arithmetic series has the property that the sum of the first ten terms is half the sum of the first sixteen terms. Also the 4th term is 14. Find the first term and common difference.
    We cant seem to figure it out and so any help or suggestions would be appreciated!
    \displaystyle\sum_{i=1}^{10} a_i=\dfrac{1}{2} \displaystyle\sum_{i=1}^{16} a_i
    Using the formula for the sum of an AP:
    \displaystyle\sum_{i=1}^n (a+(k-1)d)=\dfrac{n}{2}(2a+(n-1)d)
    on both sides of the equation should give you one equation for a and d
    Given also that a_4=a+3d=14, you have two simultaneous equations.
 
 
 
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